Questions: Graph the following function: y=3 sec (1/2(x+3π/4))+1

Solution Steps

The function given is: \[ y = 3 \sec \left(\frac{1}{2}\left(x+\frac{3 \pi}{4}\right)\right) + 1 \]

The function is in terms of \(y\) and \(x\), which indicates that it should be plotted on a Cartesian coordinate system.

To graph the function, we need to determine a suitable range for \(x\) and \(y\). Since the secant function has vertical asymptotes where the cosine function is zero, we should choose a range that avoids these points. A typical range for \(x\) might be from \(-2\pi\) to \(2\pi\), and for \(y\), we can choose a range that captures the behavior of the function, such as \(-10\) to \(10\).

Final Answer